Given ¬(p ∨ q), prove (¬p ∧ ¬q) using propositional logic operators.

Question

I believe there is a way to prove it as both terms have equal truth tables. But how using propositional logic operators ?

Answer 1

You need to prove that $\neg p$ and $\neg q$.

Assume $p$. Then $p \lor q$. That contradicts $\neg(p \lor q)$. Therefore $\neg p$.

Do the same to prove $\neg q$ and you're done.